Dispersion coding of ENZ media via multiple photonic dopants

Abstract

Epsilon-near-zero (ENZ) media are opening up exciting opportunities to observe exotic wave phenomena. In this work, we demonstrate that the ENZ medium comprising multiple dielectric photonic dopants would yield a comb-like dispersion of the effective permeability, with each magnetic resonance dominated by one specific dopant. Furthermore, at multiple frequencies of interest, the resonant supercouplings appearing or not can be controlled discretely via whether corresponding dopants are assigned or not. Importantly, the multiple dopants in the ENZ host at their magnetic resonances are demonstrated to be independent. Based on this platform, the concept of dispersion coding is proposed, where photonic dopants serve as “bits” to program the spectral response of the whole composite medium. As a proof of concept, a compact multi-doped ENZ cavity is fabricated and experimentally characterized, whose transmission spectrum is manifested as a multi-bit reconfigurable frequency comb. The dispersion coding is demonstrated to fuel a batch of innovative applications including dynamically tunable comb-like dispersion profiled filters, radio-frequency identification tags, etc.

Low‐Loss Epsilon‐Near‐Zero Metamaterials

“…Furthermore, by constructing a hollow metal‐layer resonant cavity with a gap, we implant the classic inductor‐capacitor (LC) resonance [ 41 ] into the ENZ host to tune the effective permeability, showing that the dielectric‐free approach achieves the same features as ideal lossless photonic doping. In contrast to the conventional method, [ 23,24,30 ] we have experimentally achieved the largest tuning range of the real part and the smallest imaginary part of the effective permeability in ENZ metamaterials, as well as the highest transmission efficiency. This indicates the best quality of ENZ metamaterials and boosts the concept of photonic doping from ideal cases to more extensive and practical applications.…”

“…[ 49 ] For comparison, the lossy material dopant only shows a maximum of approximately 0.5. We derive the formula for retrieving the effective relative permeability from the transmission amplitude and phase (detailed information can be found in Text S3, Supporting Information): [ 24,30 ] $$$$\begin{equation}{{{\mu}}_{{\rm{eff}}}} = {{\mu}}_{{\rm{eff}}}^{\rm{,}} - i{{\mu}}_{{\rm{eff}}}^{{\rm{,,}}} = \frac{{2 - 2/{\rm{T}}({{\omega}}) - i{\rm{T}}({{\omega}}){\varepsilon _{\rm{h}}}\omega l/(c\sqrt {{\varepsilon _{\rm{f}}}} )}}{{{\varepsilon _{\rm{h}}}{{(\omega l/c)}^2} + i\sqrt {{\varepsilon _{\rm{f}}}} \omega l/c}}\end{equation}$$$$where l = 50 mm represents the path length of electromagnetic waves, ε f = 2.1 – c 2 π 2 /( ω 2 h 2 ) is the relative permittivity of the Teflon‐filled port under the waveguide‐emulated plasma, and T(ω) = |T(ω)| e Arg[T(ω)] is the transmission coefficient. We plot the retrieved µ ′ eff in Figure 2e and | µ ″ eff / µ ′ eff | (magnetic loss tangent) [ 39,40 ] in Figure 2f.…”

“…[49] For comparison, the lossy material dopant only shows a maximum of approximately 0.5. We derive the formula for retrieving the effective relative permeability from the transmission amplitude and phase (detailed information can be found in Text S3, Supporting Information): [24,30]…”

“…A general conceptual sketch of photonic-doped ENZ metamaterials is shown in Figure 1a. By locating a dielectric impurity in an ENZ host (relative permittivity 𝜖 h ≈ 0, relative permeability µ r = 1), [23,24,30] one can tune the effective permeability of the whole ENZ metamaterial. The scale of the ENZ host can be much less than the wavelength in free space, which is an excellent platform for adjusting equivalent electromagnetic properties at deep subwavelength scales.…”

“…The scale of the ENZ host can be much less than the wavelength in free space, which is an excellent platform for adjusting equivalent electromagnetic properties at deep subwavelength scales. Regarding theoretical predictions, the real part of the permeability in ideal photonic doping systems can change from negative infinity to positive infinity, [23,30] attaining the following two special cases: an epsilon-and-mu-near-zero (EMNZ) medium [24,[31][32][33] with a near-zero permeability and a perfect magnetic conductor (PMC) body with an infinite permeability. The effective permeability of ideal systems has an imaginary part that is constantly equal to 0.…”